We have examined the effects of substituents on the computed electrostatic potentials V(S)(r) and average local ionization energies I(S)(r) on the surfaces of model carbon nanotubes of the types (5,5), (6,1) and (6,0). For the (5,5) and the (6,1), the effects upon both V(S)(r) and I(S)(r) of substituting a hydroxyl group at one end are primarily localized to that part of the system. For the (6,0) tube, however, a remarkable change is observed over its entire length, with V(S)(r) showing a marked gradation from strongly positive at the substituted end to strongly negative at the other; I(S)(r) correspondingly goes from higher to lower values. Replacing OH by another resonance- donor, NH2, produces similar results in the (6,0) system, while the resonance withdrawing NO2 does the opposite, but in equally striking fashion. We explain these observations by noting that the arrangement of the C-C bonds in the (6,0) tube facilitates charge delocalization over the full length and entire surface of the tube. Substituting NH2 and NO2 at opposite ends of the (6,0) tube greatly strengthens the gradations in both V(S)(r) and I(S)(r). The first hyperpolarizability of this system was found to be nine times that of para-nitroaniline, suggesting possible nonlinear optical applications. [figure: see text]. HF/STO-5G electrostatic potential on outer surface of open (6,0) C72H10NH2NO2. The nitro group is at the right end of the tube, the amino group at the left. In eV: purple is less than 14, blue is between 14 and 15, green is between 15 and 16.5, yellow is between 16.5 and 17.5, and red is more than 17.5.